The second topological space is the generalized cone complex \(J^{trop}_{g,n}\)  associated to \(\mathcal {J}_{g,n}^{trop}\)  (in the sense of [1]}). As a topological space \(J^{trop}_{g,n}\)  parametrizes isomorphism classes of pairs consisting of a tropical curve \(\Gamma \)  of type \((g,n)\)  and an admissible divisor \(D\)  on the underlying graph of \(\Gamma \) . Its canonical compactification \(\overline{J}^{trop}_{g,n}\)  parametrizes pairs consisting of an extended tropical curve (see Definition REF ) and an admissible divisor \(D\)  on the underlying graph \((\Gamma )\) . In Definition REF , \(J^{trop}_{g,n}\)  and \(\overline{J}^{trop}_{g,n}\)  as the colimits
\(J^{trop}_{g,n}=\varinjlim _{(G,D)\in \operatorname{\mathcal {QD}iv}_{g,n}} \mathbb {R}_{\ge 0}^{E(G)}\subset \overline{J}^{trop}_{g,n}=\varinjlim _{(G,D)\in \operatorname{\mathcal {QD}iv}_{g,n}} \big (\mathbb {R}_{\ge 0}\cup \lbrace +\infty \rbrace \big )^{E(G)},\) 
